cirq.DensePauliString

An immutable string of Paulis, like XIXY, with a coefficient.

Inherits From: BaseDensePauliString, Gate

cirq.DensePauliString(
    pauli_mask: Union[Iterable['cirq.PAULI_GATE_LIKE'], np.ndarray],
    *,
    coefficient: 'cirq.TParamValComplex' = 1
)

A DensePauliString represents a multi-qubit pauli operator, i.e. a tensor product of single qubits Pauli gates (including the cirq.IdentityGate), each of which would act on a different qubit. When applied on qubits, a DensePauliString results in cirq.PauliString as an operation.

Note that cirq.PauliString only stores a tensor product of non-identity cirq.Pauli operations whereas cirq.DensePauliString also supports storing the cirq.IdentityGate.

For example,

dps = cirq.DensePauliString('XXIY')
print(dps) # 4 qubit pauli operator with 'X' on first 2 qubits, 'I' on 3rd and 'Y' on 4th.
+XXIY
ps = dps.on(*cirq.LineQubit.range(4)) # When applied on qubits, we get a `cirq.PauliString`.
print(ps) # Note that `cirq.PauliString` only preserves non-identity operations.
X(q(0))*X(q(1))*Y(q(3))

This can optionally take a coefficient, for example:

dps = cirq.DensePauliString("XX", coefficient=3)
print(dps) # Represents 3 times the operator XX acting on two qubits.
(3+0j)*XX
print(dps.on(*cirq.LineQubit.range(2))) # Coefficient is propagated to `cirq.PauliString`.
(3+0j)*X(q(0))*X(q(1))

If the coefficient has magnitude of 1, the resulting operator is a unitary and thus is also a cirq.Gate.

Note that DensePauliString is an immutable object. If you need a mutable version of dense pauli strings, see cirq.MutableDensePauliString.

pauli_mask A specification of the Pauli gates to use. This argument can be a string like "IXYYZ", or a numeric list like [0, 1, 3, 2] with I=0, X=1, Y=2, Z=3=X|Y.

The internal representation is a 1-dimensional uint8 numpy array containing numeric values. If such a numpy array is given, and the pauli string is mutable, the argument will be used directly instead of being copied.

coefficient A complex number. Usually +1, -1, 1j, or -1j but other values are supported.

coefficient A complex coefficient or symbol.
pauli_mask A 1-dimensional uint8 numpy array giving a specification of Pauli gates to use.

Methods

controlled

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controlled(
    num_controls: Optional[int] = None,
    control_values: Optional[Union[cv.AbstractControlValues, Sequence[Union[int, Collection[int]]]]
        ] = None,
    control_qid_shape: Optional[Tuple[int, ...]] = None
) -> 'Gate'

Returns a controlled version of this gate. If no arguments are specified, defaults to a single qubit control.

Args
num_controls Total number of control qubits.
control_values Which control computational basis state to apply the sub gate. A sequence of length num_controls where each entry is an integer (or set of integers) corresponding to the computational basis state (or set of possible values) where that control is enabled. When all controls are enabled, the sub gate is applied. If unspecified, control values default to 1.
control_qid_shape The qid shape of the controls. A tuple of the expected dimension of each control qid. Defaults to (2,) * num_controls. Specify this argument when using qudits.

Returns
A cirq.Gate representing self controlled by the given control values and qubits. This is a cirq.ControlledGate in the base implementation, but subclasses may return a different gate type.

copy

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copy(
    coefficient: Optional[Union[sympy.Expr, int, float, complex]] = None,
    pauli_mask: Union[None, str, Iterable[int], np.ndarray] = None
) -> 'DensePauliString'

Returns a copy with possibly modified contents.

Args
coefficient The new coefficient value. If not specified, defaults to the current coefficient value.
pauli_mask The new pauli_mask value. If not specified, defaults to the current pauli mask value.

Returns
A copied instance.

eye

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@classmethod
eye(
    length: int
) -> Self

Creates a dense pauli string containing only identity gates.

Args
length The length of the dense pauli string.

frozen

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frozen() -> 'DensePauliString'

A cirq.DensePauliString with the same contents.

mutable_copy

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mutable_copy() -> 'MutableDensePauliString'

A cirq.MutableDensePauliString with the same contents.

num_qubits

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num_qubits() -> int

The number of qubits this gate acts on.

on

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on(
    *qubits
) -> 'cirq.PauliString'

Returns an application of this gate to the given qubits.

Args
*qubits The collection of qubits to potentially apply the gate to.

Returns: a cirq.Operation which is this gate applied to the given qubits.

on_each

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on_each(
    *targets
) -> List['cirq.Operation']

Returns a list of operations applying the gate to all targets.

Args
*targets The qubits to apply this gate to. For single-qubit gates this can be provided as varargs or a combination of nested iterables. For multi-qubit gates this must be provided as an Iterable[Sequence[Qid]], where each sequence has num_qubits qubits.

Returns
Operations applying this gate to the target qubits.

Raises
ValueError If targets are not instances of Qid or Iterable[Qid]. If the gate qubit number is incompatible.
TypeError If a single target is supplied and it is not iterable.

one_hot

View source

@classmethod
one_hot(
    *, index: int, length: int, pauli: 'cirq.PAULI_GATE_LIKE'
) -> Self

Creates a dense pauli string with only one non-identity Pauli.

Args
index The index of the Pauli that is not an identity.
length The total length of the string to create.
pauli The pauli gate to put at the hot index. Can be set to either a string ('X', 'Y', 'Z', 'I'), a cirq gate (cirq.X, cirq.Y, cirq.Z, or cirq.I), or an integer (0=I, 1=X, 2=Y, 3=Z).

sparse

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sparse(
    qubits: Optional[Sequence['cirq.Qid']] = None
) -> 'cirq.PauliString'

A cirq.PauliString version of this dense pauli string.

Args
qubits The qubits to apply the Paulis to. Defaults to cirq.LineQubit.range(len(self)).

Returns
A cirq.PauliString with the non-identity operations from this dense pauli string applied to appropriate qubits.

Raises
ValueError If the number of qubits supplied does not match that of this instance.

tensor_product

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tensor_product(
    other: 'BaseDensePauliString'
) -> Self

Concatenates dense pauli strings and multiplies their coefficients.

Args
other The dense pauli string to place after the end of this one.

Returns
A dense pauli string with the concatenation of the paulis from the two input pauli strings, and the product of their coefficients.

validate_args

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validate_args(
    qubits: Sequence['cirq.Qid']
) -> None

Checks if this gate can be applied to the given qubits.

By default checks that:

  • inputs are of type Qid
  • len(qubits) == num_qubits()
  • qubit_i.dimension == qid_shape[i] for all qubits

Child classes can override. The child implementation should call super().validate_args(qubits) then do custom checks.

Args
qubits The sequence of qubits to potentially apply the gate to.

Raises
ValueError The gate can't be applied to the qubits.

with_probability

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with_probability(
    probability: 'cirq.TParamVal'
) -> 'cirq.Gate'

Creates a probabilistic channel with this gate.

Args
probability floating point value between 0 and 1, giving the probability this gate is applied.

Returns
cirq.RandomGateChannel that applies self with probability probability and the identity with probability 1-p.

wrap_in_linear_combination

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wrap_in_linear_combination(
    coefficient: Union[complex, float, int] = 1
) -> 'cirq.LinearCombinationOfGates'

Returns a LinearCombinationOfGates with this gate.

Args
coefficient number coefficient to use in the resulting cirq.LinearCombinationOfGates object.

Returns
cirq.LinearCombinationOfGates containing self with a coefficient of coefficient.

__abs__

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__abs__() -> Self

__add__

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__add__(
    other: Union['Gate', 'cirq.LinearCombinationOfGates']
) -> 'cirq.LinearCombinationOfGates'

__call__

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__call__(
    *qubits, **kwargs
)

Call self as a function.

__eq__

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__eq__(
    other: _SupportsValueEquality
) -> bool

__getitem__

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__getitem__(
    item
)

__iter__

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__iter__() -> Iterator[Union['cirq.Pauli', 'cirq.IdentityGate']]

__len__

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__len__() -> int

__mul__

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__mul__(
    other
)

__ne__

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__ne__(
    other: _SupportsValueEquality
) -> bool

__neg__

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__neg__()

__pos__

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__pos__()

__pow__

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__pow__(
    power: Union[int, float]
) -> Union[NotImplementedType, Self]

__rmul__

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__rmul__(
    other
)

__sub__

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__sub__(
    other: Union['Gate', 'cirq.LinearCombinationOfGates']
) -> 'cirq.LinearCombinationOfGates'

__truediv__

View source

__truediv__(
    other
)

I_VAL 0
X_VAL 1
Y_VAL 2
Z_VAL 3